CHAPTER 6: ELECTRONIC STRUCTURE

– The Nature of Light – Quantized Energy/Photons –Photoelectric Effect – Bohr’s Model of Hydrogen – Wave Behavior of Matter –Uncertainty Principle – Quantum Mechanics/Atomic Orbitals –Quantum Numbers/Orbitals

– Representations of Orbitals – Many-Electron Atoms –Effective Nuclear Charge –Relative Energies of Orbitals –Electron Spin/Pauli Excl. Principle – Electron Configurations – Periodic Relationships

Wave Nature of Light Electromagnetic Radiation –electric & magnetic components with periodic oscillations –length in m, cm, mm,  m, nm, –frequency in cycles/sec or hertz, – = c where c = speed of light

long wavelength short wavelength

Quantized Energy and Photons Black Body Radiation –heated bodies radiate light and depends on temperature –Planck -- energy released in ‘packets’ – smallest ‘packet’ is a quantum –energy of one quantum, E =  , Planck’s constant = 6.63 x J-s

Practice Ex. 6.2: A laser that emits light in short pulses has a = 4.69 x s -1 and deposits 1.3 x J of energy during each pulse. How many quanta of energy does each pulse deposit? E =  E of 1 quantum = (6.63 x J-s) (4.69 x s -1 ) = 3.11 x J/quanta 1.3 x J = 4.2 x quanta 3.11 x J/quanta

Photoelectric Effect –metals exposed to light, radiant energy, emit electrons –each metal has a minimum of light –Einstein’s ‘ photons ’ of light must have sufficient threshold energy –energy of photon depends on the of light, E =  high frequency, short wavelength ( = c/ )  high energy –light is also quantized, 1 photon = 1 quanta

metal surface photon with E > threshold e - with kinetic energy = photon E - threshold E e -

Bohr’s Model of the Hydrogen Atom Line Spectra –spectrum -- light composed of different wavelengths and energies –contiunous spectrum -- continuous range of ’s and E’s –line spectrum -- non-continuous spectrum (only specific ’s and E’s) –Balmer 1800’s = C (1/ /n 2 ) n = 3, 4, 5, 6 C = 3.29 x s - 1

Hydrogen Line Spectrum

Bohr’s Model –electrons in “orbits” around nucleus –“orbits” are allowed energies which are quantized –to move between quantized orbits, electrons must either absorb or emit quanta of energy –E = - R H ( 1/n 2 ) n = 1, 2, 3, principle quantum number – R H (Rydberg constant) = 2.18 x J

e-e- e-e- nucleus n=1n=2n=3n=4 e-e- Energy absorption

nucleus e-e- e-e- n=1n=2n=3n=4 Energy emission

e-e- e-e- nucleus n=1 n=2 n=3 n=4 E1E1 E2E2 E3E3  E = E f - E i =   E 1 >  E 2 >  E 3

–energy of the transition depends on the levels  E = E f - E i =  or  E = = E f - E i  = (R H /  )(1/n i 2 - 1/n f 2 ) or  E = R H (1/n i 2 - 1/n f 2 ) n i = initial level of electron n f = final level of electron

 E or is + radiant energy absorbed nucleus n=1n=2n=3n=4  E or is - radiant energy emitted

n= Balmer Series - visible H line spectrum H Lyman Series - in the uv

Wave Behavior of Matter Basis for Quantum Mechanics – De Broglie wave equation =  “matter” waves mv –Uncertainty Principle -- Werner Heisenberg fundamental limitation on how precisely we can know the location and momentum

Quantum Mechanics and Atomic Orbitals Quantum Mechanics or Wave Mechanics –mathematical method of predicting the behavior of electrons –wave functions are solutions to these mathematical equations –wave functions predict the “ probability ” of finding electron density,  2 –wavefunction describes “orbitals”

Orbitals & Quantum Numbers –orbitals describe volumes of electron density –orbitals are of different types s, p, d, f –each orbital is described by a set of quantum numbers n,, m each quantum number has an allowed set of values

Quantum Numbers n  can have values of 1, 2, 3, 4, – describes the major shell or distance from the nucleus  can have values of 0, 1, 2, 3... n-1 –describes the type of subshell = 0 s subshell = 1 p subshell = 2 d subshell = 3 f subshell m  can have values of –describes which orbital within the subshell

n=1n=2 nucleus + s s p p p s p p p d d d d d s p p p d d d d d f f f f f f f n=4n=3 s p d f = 0 = 1 = 2 = 3

–total number of orbitals in a subshell is n 2 –maximum number of electrons in a subshell is 2n 2 –maximum number of electrons in an orbital is 2 s  last quantum number describes the spin on an electron –each electron has a spin +½ or -½

n=1n=2 nucleus + s s p p p s p p p d d d d d s p p p d d d d d f f f f f f f n=4n=3 s p d f = 0 = 1 = 2 = m m m m

Orbital Pictures s-type orbitals –always one orbital in the subshell with = 0 and m = 0 –are spherical –differences between s orbitals in different major shells (with different n values) size –remember, we’re talking in terms of probability of the occurrence of electron density

Notice that we are looking at a volume of diffuse electron electron density as pictured by the many small dots

s orbital cross- sections

p-type orbitals –always three orbitals in the subshell with = 1 and m = -1, 0, +1 –are dumb-bell shaped –different m values are oriented along different axes, x, y, or z (p x, p y, p z ) –differences between p orbitals in different major shells size

d-type orbitals –always five orbitals in the subshell with = 2 and m = -2, -1, 0 +1, +2 –most are four-lobed –different m values are oriented differently on x, y, z axes d z 2, d x 2 -y 2, d xy, d xz, d yz –differences between d orbitals in different major shells size

Energy s s p pp s d dddd d dddd f ffffff p pp Orbital/Subshell energy levels in the hydrogen atom n=1 s p pp n=2 n=3 n=4

Multi-electron Atoms screening effect –inner electrons “shield” the nuclear charge from outer electrons –energy levels of subshells within major shells become different –nuclear charge experience by outer electrons is decreased Z eff = Z - S Z eff decreases with increasing value

Energy s Orbital/Subshell energy levels in multi electron atoms n=1 s p pp n=2 s n=3 n=2 p pp n=3 d dddd

Pauli Exclusion Principle –no two electrons can have the same exact set of quantum numbers consider this orbital and its two electrons quantum numbers are n = 2, = 1, m = 0 the two electrons must have a quantum number that is different -- s = +½ and - ½ –First electron has spin +½ and second electron -½ p pp n=2  = 1 m =

Electron Configurations There is a pattern in the energy levels that hold electrons –electrons fill up the pattern from the lowest energy to the highest energy level –1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s –for 1 H  for 2 He  1s 1s – 3 Li   4 Be  1s 2s 1s 2s

Hund’s Rule –electrons enter degenerate orbitals in a subshell one at a time until the subshell is half-filled – 5 B   6 C   1s 2s 2p 1s 2s 2p – 7 N   1s 2s 2p – 8 O   1s 2s 2p

Periods 1, 2 & 3 – 3 Li  1s 2s – 11 Na    1s 2s 2p 3s – 19 K    1s 2s 2p 3s 3p 4s –outer shell is called the valence shell

Group 1 – 3 Li  1s 2s – 11 Na    1s 2s 2p 3s – 19 K    1s 2s 2p 3s 3p 4s [Ne] [Ne] 3s 1 [Ar] [Ar] 4s 1

–all group I elements have electron configuration [nobel gas] ns 1 –all group II elements have electron configuration [nobel gas] ns 2 –all group III elements have electron configuration [nobel gas] ns 2 np 1 –group IV elements [nobel gas] ns 2 np 2 –group V elements [novel gas] ns 2 np 3 etc.

s 1 s 2 p 3 p 4 p 5 p 6 p 7 p d d 10 Electron Configuration & Periodic Table ns 1 ns 2 ns 2 p 1 ns 2 p 2 ns 2 p 3 ns 2 p 4 ns 2 p 5 ns 2 p 6 ns 2 (n-1)d 1-10